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A finite basis theorem for residually finite, congruence meet-semidistributive varieties

Published online by Cambridge University Press:  12 March 2014

Ross Willard
Ross Willard*
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada, E-mail: rdwillar@gillian.math.uwaterloo.ca
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Abstract

We derive a Mal'cev condition for congruence meet-semidistributivity and then use it to prove two theorems. Theorem A: if a variety in a finite language is congruence meet-semidistributive and residually less than some finite cardinal, then it is finitely based. Theorem B: there is an algorithm which, given m < ω and a finite algebra in a finite language, determines whether the variety generated by the algebra is congruence meet-semidistributive and residually less than m.

Keywords

equational theoryfinitely basedresidually finitevarietycongruence meet-semidistributive
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 1 , March 2000 , pp. 187 - 200
Copyright
Copyright © Association for Symbolic Logic 2000

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